Having been given the lengths, *a* and *b,* of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the lengths of those sides.

Click here to reveal the answer.

The answer is: For \(a\) between \(\frac{b}{2}\) and \(2b,\) or, equivalently, for \(b\) between \(\frac{a}{2}\) and \(2a,\) \[x=2\sqrt{\frac{4b^2-a^2}{15}}\quad{\rm and}\quad y=2\sqrt{\frac{4a^2-b^2}{15}}.\]